Transient Groundwater Analysis
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Transient Groundwater Analysis
A transient groundwater analysis may be important when there is a
time-dependent change in pore pressure. This will occur when
groundwater boundary conditions change and the permeability of the
material is low. In this case, it will take a finite amount of time to reach
steady state flow conditions. The transient pore pressures may have a
large effect on slope stability.
This tutorial describes how to perform a transient groundwater analysis
in Slide using finite elements. A subsequent tutorial will describe how
this affects slope stability calculations.
The finished product of this tutorial can be found in the Tutorial 18
Transient Groundwater.slim data file. All tutorial files installed with
Slide 6.0 can be accessed by selecting File > Recent Folders > Tutorials
Folder from the Slide main menu.
Topics Covered
•
Finite element groundwater seepage analysis
•
Transient groundwater
Geometry
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Model
Start the Slide Model program.
Project Settings
Open the Project Settings dialog from the Analysis menu. Set the
Stress Units to Metric, set the Time Units to Hours and the Permeability
Units to meters/second as shown.
Click on the Groundwater link on the left side. Leave the Method as
Water Surfaces. Select the Advanced checkbox and choose Transient
Groundwater.
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The Method refers to the method used to obtain the initial state for the
transient groundwater analysis. In this tutorial we will simply specify an
initial water table but it is also possible to specify a grid of pore pressures
or even to perform a steady state finite element analysis to get the initial
state. This is discussed further in subsequent tutorials.
Now click on the Transient link on the left. Here we need to specify the
times at which we wish to observe pore pressure results. Change the
Number of Stages to 5. Enter the times for each stage as shown.
Do not check the boxes to Calculate SF (safety factor). In this tutorial we
will only look at the groundwater modelling. A subsequent tutorial will
combine this with slope stability calculation.
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Click OK to close the Project Settings dialog.
You will now see a blank screen with two tabs at the bottom. One for
Slope Stability and one for Transient Groundwater. The first part of this
tutorial involves setting up the model geometry. This can only be done in
the Slope Stability mode, so click on the tab for Slope Stability.
Boundaries
The model represents a dam with a toe drain. Here we will define the
geometry of the problem.
Make sure that you are in ‘Slope Stability’ view. Select the Add
External Boundary option in the Boundaries menu and enter the
following coordinates:
0,0
20 , 10
24 , 12
28 , 12
52 , 0
40 , 0
c (to close the boundary)
Hit Enter to finish entering points. The model will look like this:
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Materials
Select Define Materials from the Properties menu. Change the name
of Material 1 to Soil. The rest of the parameters we don’t care about since
we are only performing a groundwater analysis, so leave them with the
default values. We will set the groundwater flow parameters later.
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Click OK to close the dialog.
By default, the entire dam is set to Material 1 (Soil), so we do not need to
assign any material properties.
Initial water table
In the Slope Stability view, you can also specify the initial water table
that exists prior to the transient groundwater analysis. For this tutorial
we will assume that the initial water table is at the base of the dam, so
we don’t need to specify it. If no water table is specified then all points
will have an initial pore pressure of 0.
Groundwater
Now it is time to set up the finite element model for calculation of
transient groundwater behaviour, so select the tab for Transient
Groundwater at the bottom of the screen.
Mesh
Before we can set up the boundary conditions we need to create a finite
element mesh. This is easily done by selecting Mesh → Discretize and
Mesh. The model should now look like this:
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Boundary Conditions
We will set up boundary conditions to simulate rapid filling of the dam on
the left side and drainage from the toe drain at the bottom right.
Select Mesh → Set Boundary Conditions. For BC Type choose Total
Head and set the Total Head Value to 10 m.
Click on the left side of the slope near the bottom and click Apply. The
model should look like this:
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Now for BC Type choose Zero Pressure. Click on the horizontal section at
the bottom right of the model (the toe drain). Click Apply. Click Close,
and the model should look like this:
Material Properties (Groundwater)
Select Properties → Define Hydraulic Properties. The hydraulic
properties required for a transient analysis are the same as those for a
steady state analysis except that a water content curve (WC) must now
be specified.
Here you can choose from a number of possible curves that relate
permeability and water content to negative pore pressure (suction). For
this tutorial, we will define our own relationship.
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Click the New button to define a new function. Change the Name to Soil
Curve. Ensure that the Permeability tab is selected and enter the values
as shown.
You can see the permeability will be 1e-7 m/s until the suction exceeds 15
kPa, at which time the permeability decreases with increasing suction.
We now need to define the relationship between water content and
suction. The volumetric water content (θ) is the volume of water as a
proportion of the total volume (θ = Vw/VT). You can also think of it as the
porosity times the degree of saturation (θ = φSw) where the degree of
saturation ranges from 0 (dry) to 1 (saturated).
Click the Water Content tab. Enter the values as shown.
You can see that at 0 matric suction, the water content is 0.4. If we
assume the material is 100% saturated at this pressure, then this
suggests a porosity of 0.4. As the matric suction increases, the water
content decreases, suggesting a decrease in saturation.
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Click OK to close the dialog.
In the Define Hydraulic Properties dialog, ensure that Soil Curve is the
chosen Model. Leave all other values as default.
Click OK to close the dialog.
Compute
Save the model using the Save As option in the File menu. Choose
Compute (groundwater) from the Analysis menu to perform the
analysis. When it is finished, choose Interpret (groundwater) from the
Analysis menu to view the results.
Interpret
You will first see the initial state. All pore pressures are 0. Click on the
tab for Stage 1 (10 hours). You will now see the pressure head for Stage 1
(10 hours).
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You can see how the rapid rise in water level at the left edge has induced
high pore pressures along the left flank but the water has not yet flowed
through the dam to increase pressures elsewhere.
Click through the other stages using the tabs at the bottom. You will see
the progression of the groundwater with time, and in particular the
changing of the water table (pink line).
Click on the tab for Stage 5 (10000 hours). This essentially represents the
steady state. You can show the progression of the water table with time
by going to View → Display Options. Select the Groundwater tab and
under FEA water, select All Stages as shown.
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Click Done. The plot will now look like this:
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You can see that the solid pink line represents the water table at 10,000
hours and the dashed pink lines represent the water table at other
stages. Go back to the Display Options and turn off the water tables.
Show the flow vectors by clicking on the Show Flow Vectors button in the
tool bar. The plot will look like this.
You can see the flow of water towards the toe drain on the bottom right.
If you click through the stage tabs again, you will see the progression of
flow through the dam with time.
We can look at the change in pressure with time in more detail by using a
query. Go to Groundwater → Query → Add Material Query. We
want to examine a single point near the middle of the dam, so enter the
coordinates 25 , 5. Hit Enter to finish entering points. Uncheck Show
Queried Values as shown.
Click OK.
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You will now see a + near the middle of the dam indicating the query
point (you may need to turn off the flow vectors to see it). Right click on
the + and select Graph Data vs. Time. You will now see a plot of
pressure head versus time at that location.
It is often more informative to use the logarithm of time. To do this, go to
Chart → Chart Properties. Expand the Axes item and change
Logarithmic Horizontal Scale to Yes as shown.
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Click Close. The chart will now look like this:
You can see how the pressure front didn’t reach the point until about 100
hours after the raising of the water level, and that after 100 hours, the
pressure head climbed to its steady state value of ~2.4 m at 10,000 hours.
This concludes the tutorial.
Additional Exercise
You may want to see if 10,000 hours represents the true steady state. You
can do this in two ways:
1. Add another stage at some later time (say 20,000 hours) and see
if there is any change
2. Run a steady state (non-transient) analysis and see if you get the
same result.
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